On Self-Dual Yang-Mills Theory

We shall discuss a first-order gauge theory whose equations of motion are the self-duality equations. There are reasons to regard this theory as a "part" of standard YM Lagrangian responsible for "mostly plus" scattering amplitudes. The quantum properties of this self-dual theory are peculiarly simple, but still instructive, and hint at a possible complete solvabillity. This type of theory, on one hand, can be related to a certain limit of (twisted) N=2 super Yang-Mills theory, while, on the other hand, it is equivalent to a holomorphic Chern-Simons type theory on twistor space classically and presumably quantum mechanically.